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Assessing the Identifiability of Models for Monoclonal Antibody Target Mediated Drug Disposition Using a New Metric of Potency

Andy Stein, Prasad Ramakrishna

Pharmacometrics, Novartis - July 13, 2016

+

Complex

t1/2 ≈ 21d

t1/2 ≈ 1h

t1/2 ≈ 21d

Drug

Target

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Overview

  • Introduction to monoclonal antibody drugs.
  • Present model for describing kinetics of monoclonal antibody drug and its target
  • Analyze mathematical model to
    • 1) Identify nondimensional potency factor for target inhibition

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    • 2) Assess the identifiability of the model

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INTRODUCTION

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Monoclonal Antibodies with Soluble Targets

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+

Complex

t1/2 ≈ 21d

t1/2 ≈ 1h

t1/2 ≈ 21d*

Drug

Target

* Drug and complex do not necessarily have the same half-life

Total Target Assay

Measures both free and bound target

Binding neutralizes the target

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Drug Pharmacokinetics for 150 mg monthly subcutaneous dosing

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Drug Conc.

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Target accumulation is 200x and drug is in vast excess to its target.

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15,000:1

150 nM = 22 μg/ml Cmin

for 150 mg Drug

0.01 nM (Post-dose steady state target)

5×10-5 nM (Baseline target conc.)

200x accumulation

Drug Conc.

Target

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Target accumulation is similar for both �150 mg and 300 mg

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15,000:1

150 nM = 22 μg/ml Cmin

for 150 mg Drug

0.01 nM (Post-dose steady state target)

5×10-5 nM (Baseline target conc.)

200x accumulation

Question: What would you predict for efficacy?

Drug Conc.

Target

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Greater efficacy is observed at 300 mg vs 150 mg Why?

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Total Target Data

Similar for 150 mg and 300 mg

PASI2 90 Efficacy Metric

Superior for 300 mg

Week

Week

Conc. (nM)

300 mg

150 mg

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MATHEMATICAL MODEL OF DRUG-TARGET BINDING

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The PK-binding model

  • Assumption: Target binding and synthesis in the peripheral compartment.
    • This assumption is made out of convenience: data is not rich enough to identify additional peripheral parameters.

| Binding Models in Drug Dev. | A. Stein | June 2016 | TMDP | Business Use Only

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Drug (D)

+

Target (T)

Complex (DT)

Dose

ksyn

keD

keT

keDT

kon

koff

Drug-Periph (DP)

k12

k21

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The PK-binding model equations

  • Not all parameters of this model are identifiable.
  • We only measure total target, which is the sum: Ttot = T + DT

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Drug (D)

+

Target (T)

Complex (DT)

Dose

ksyn

keD

keT

keDT

Dose or Synthesis

Elimination

Binding

Distribution

kon

koff

k12

k21

Drug-Periph (DP)

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The Quasi-Equilibrium Assumption

  • Assumption: binding is rapid such that drug, target, and complex stay in equilibrium.

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  • This assumption allows us to reduce number of state variables from four [D, T, DT, DP] to three [Dtot, Ttot, DP] plus an algebraic set of equations

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The Quasi-Equilibrium Model�Binding only occurs in central compartment

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Dose or Synthesis

Elimination

Distribution

Drug (D)

+

Target (T)

Complex (DT)

Dose

ksyn

keD

keT

keDT

Drug-Periph (DP)

Kd

Concentrations D, T, and DT are solved for using

algebraic binding equations

k12

k21

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Model fit to drug PK and target accumulation data

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Total Target Concentration

(subcutaneous dosing)

150 mg

700 mg

Drug Concentration

(700 mg iv dosing)

0 3 6 9 12

Time (Weeks)

60

50

40

30

20

10

0

Conc. (ng/ml)

Model can be used to:

1) Describe available PK and total target data.

2) Predict free target concentration

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Sensitivity analysis: total target plateaus, but free target continues to decline with dose

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Above 150 mg,

total target concentration

plateaus

(measurable)

Above 150 mg,

every 2x dose increase leads to 2x free target decrease

(predicted)

150 mg

27% free

300 mg

14% free

subcutaneous

dosing

2 compartment linear PK with subcutaneous absorption

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MATHEMATICAL ANALYSIS OF DRUG-TARGET MODEL

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Key Quantity of Interest: Free Target vs Baseline

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2) Total Target

Accumulation

1) Free Target

vs Total Target

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Calculating Free Target vs Total Target

  • Algebraic manipulation of quasi-equilibrium equation

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1) Free Target

vs Total Target

 

When Dtot >> Ttot, Kd

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Analysis of total target dynamics before dosing

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At steady state: dTtot/dt = 0

Before Dose, DT=0

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Analysis of total target dynamics �after dosing

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Tacc

At steady state: dTtot/dt = 0

For large drug conc.,

most target is bound,

T ≈ 0, and DT ≈ Ttot

2) Total Target

accumulation

Ttot

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Estimating the free target compared to baseline

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Summary

  • Three key parameters determine target inhibition when there is a large excess of drug relative to target at steady state.
    • Binding affinity (Kd)
    • Target accumulation factor (Tacc)
    • Drug concentration (Cavg)
  • In these circumstances, doubling dose, halving dosing interval, or halving Kd reduces free target by 50%
  • At high doses, total target reaches plateau. This does not mean target inhibition has reached plateau

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ANALYSIS OF TOTAL TARGET KINETICS

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Target dynamics is characterized by 4 parameters

  • To understand identifiability, it’s useful to reparameterize:
    • T0 = ksyn/keT
    • Ttotss = ksyn/keDT
    • keDT
    • Kd

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Drug (D)

+

Target (T)

Complex (DT)

Dose

ksyn

keD

keT

keDT

Drug-Periph (DP)

Kd

k12

k21

  • Ttot ≈ T0 + (Ttot,ss-T0)·exp[-keDT · t]

for large drug concentrations

dTtot/dt ≈ ksyn – keDT·Ttot

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Understanding the total target dynamics

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ksyn

Ttotss

T0

Dose/Kd (mg/nM)

 

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Identifiability – free target inhibition can be predicted even if baseline target is not measurable

  • Assay may not be sensitive enough to measure T0.
  • In that case, only three parameters may be identifiable:
    • keDT, Ttotss, and T0/Kd
  • Note that free target inhibition (T/T0) depends on the ratio T0/Kd
    • T/T0 = Kd·Tacc/Cavg
    • = (Kd/T0)·Ttotss/Cavg

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Varying T0,

keeping T0/Kd fixed

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Free target inhibition can be predicted even if complex elimination (keDT) is not identifiable

  • keDT is also not identifiable if sufficient samples are not taken.
  • But T/T0 can still be estimated
    • T/T0 = Kd·Tacc/Cavg
    • = (Kd/T0)·Ttotss/Cavg

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keDT

Ttotss

T0

~Dose·T0/Kd

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Summary

  • Three key parameters determine target inhibition when there is a large excess of drug relative to target at steady state.
    • Binding affinity (Kd)
    • Target accumulation factor (Tacc)
    • Drug concentration (Cavg)
  • In these circumstances, doubling dose, halving dosing interval, or halving Kd reduces free target by 50%
  • At high doses, total target reaches plateau. This does not mean target inhibition has reached plateau
  • Free target inhibition is estimable even when baseline target (T0) or rate of complex elimination (keDT) are not estimable.

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Limitations

  • This analysis focused on inhibition in blood. Inhibition in tissue is more challenging to measure and predict.

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  • This analysis only applies when drug is in vast excess to target (not applicable for anti-C5, where C5 ≈ 500 nM)

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Acknowledgements

  • Brian Stoll
  • Gerard Bruin
  • Irina Koroleva
  • Frank Kolbinger
  • Max Woisetschlaeger

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  • Henning Schmidt
  • Jean-Louis Steimer
  • Phil Lowe
  • Mick Looby
  • Karthik Subramanian
  • Bruce Gomes
  • Wenping Wang